A342773 Numbers k such that k + sum of digits of k is a proper prime power.

2, 4, 8, 17, 18, 25, 38, 72, 118, 121, 161, 234, 245, 275, 329, 347, 521, 614, 720, 830, 944, 998, 1016, 1318, 1355, 1664, 1829, 2041, 2169, 2183, 2189, 2384, 2786, 3115, 3464, 3710, 4082, 4472, 4891, 4900, 5027, 5315, 6230, 6543, 6836, 7889, 8173, 10190, 10592, 10601, 11435, 11858, 12154, 12752

Offset: 1

Author

J. M. Bergot and Robert Israel, Mar 21 2021

Keywords

• nonn
• base

Comments

Numbers k such that A062028(k) is in A246547.

Proper prime powers in the sequence include 4, 8, 25, 121. Are there any others?

Examples

			a(4) = 17 is a term because 17+1+7 = 25 = 5^2.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1001

Crossrefs

Cf. A062028, A246547. Contains A242368.

Programs

Maple

filter:= proc(n) local s,F;
   s:= n + convert(convert(n,base,10),`+`);
   F:= ifactors(s)[2];
   nops(F)=1 and F[1][2]>1
end proc:
select(filter, [$1..20000]);

PARI

isok(k) = isprimepower(k + sumdigits(k)) > 1; \\ Michel Marcus, Mar 22 2021